The polarization of American politics now extends to the issue of whether interest rates should be determined by mathematical formulas.

The House Financial Services Committee on Thursday discussed a bill that would, among other things, require the Federal Reserve to adopt a formal rule to guide monetary policy decisions to tighten or ease credit. An oft-cited model is the “Taylor rule,” which calculates changes in the benchmark federal funds rate based on measures of inflation and economic output.

“I don’t think this should be a partisan issue in any way,” said Stanford University economist John Taylor, namesake of the rule, as he testified in support of the legislation.

But it is. Republicans introduced the bill this week and expressed support for it Thursday as a sensible move to improve transparency and performance at the central bank. Democrats condemned it as an assault on the Fed’s independence.

A “clear, predictable rule” for policy would be “free from political micromanagement,” said Rep. Jeb Hensarling (R., Texas), the panel’s chairman. The Fed’s “independence and discretion must be paired with appropriate transparency and accountability,” he added.

The committee’s top Democrat, California Rep. Maxine Waters, countered that the bill would “cripple the Federal Reserve’s ability to promote growth, stabilize the economy and, at times of extraordinary crisis, take decisive action to avoid an economic collapse.”

The stark divide isn’t surprising, said Sarah Binder, a senior fellow at the Brookings Institution and professor of political science at George Washington University. “This degree of partisanship, and what people called the ‘polarization of parties,’ really seeps into all aspects of policy,” she said. “I see these disagreements as emblematic of the parties’ different positions on, ‘how do you improve the state of the economy?’”

Public criticism of the Fed has grown louder since the 2008 financial crisis, when the central bank began engaging in high-profile and unconventional policies intended to stabilize the financial system and, subsequently, to bolster the U.S. economy.

Attitudes toward the Fed’s leaders have become more polarized along party lines. When Chairman Alan Greenspan left office in 2006, he was popular among Democrats, Republicans and independents. When Chairman Ben Bernanke stepped down early this year, a Gallup poll found a majority of Democrats approved of him while a majority of Republicans disapproved.

Congressional Republicans have led a number of efforts in recent years to overhaul the Fed or open its operations to greater scrutiny. A bill that would have led to an audit of the central bank’s policy deliberations passed the House in 2012 with bipartisan support but died in the Senate without a vote.

The bill introduced this week would allow the Government Accountability Office to audit the Fed’s monetary policy discussions if the Fed doesn’t adopt a proper rule for interest rates. The chair of the Fed also could be called before Congress to explain changes to the rule or if the GAO determines the rule doesn’t comply with the law.

“This is worse than monetary policy by Congress. This is monetary policy by some sort of Spanish Inquisition,” said Massachusetts Institute of Technology economist Simon Johnson, the only opponent of the bill to testify Thursday.

The House committee didn’t invite anyone from the Fed to testify, though Chairwoman Janet Yellen is scheduled to appear before the panel next week for separate testimony.

The central bank’s leaders have long opposed lawmakers’ proposals to audit the Fed’s monetary policy deliberations, arguing it would undermine the central bank’s traditional independence from political interference.

The Fed also has signaled it doesn’t want to rely on a strict formula for setting policy. In June 2012, as the Fed’s No. 2, Ms. Yellen said, while “simple rules” like the Taylor rule “provide a useful starting point in determining appropriate policy, they by no means deserve the ‘last word’–especially in current circumstances.” She said such rules “significantly understate the case for keeping policy persistently accommodative in current circumstances.”

In any case, the bill discussed Thursday may not go far. Even if it passed the GOP-majority House, it likely would falter in the Senate, where Democrats are in control. The equation could shift, however, if Republicans gain a Senate majority in November.

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